JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (3): 77-84.doi: 10.6040/j.issn.1671-9352.0.2022.304

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A mollification method with a posteriori parameter selection for solving the Cauchy problem of the Helmholtz equation

LI Zhen-ping1,2, YU Ya-hui1*   

  1. 1. Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471023, Henan, China;
    2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2023-03-02

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Abstract: In order to restore the stability of the solution, a mollification regularization method with a posteriori selection of regularization parameter based on Gaussian kernel function is proposed. The stability error estimate between the exact solution and its approximation solution is obtained. Numerical experiments are carried out to verify the effectiveness of the proposed method.

Key words: Cauchy problem for the Helmholtz equation, mollification method, posteriori parameter selection, error estimate

CLC Number: 

  • O241.82
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